Regular Polygon Calculator
Compute the area, perimeter, interior angles, apothem, and circumradius of any regular polygon. Enter the number of sides (3 to 100) and the side length to get instant results.
A regular polygon has all sides equal and all interior angles equal. Common examples include the equilateral triangle (3 sides), square (4), regular pentagon (5), regular hexagon (6), and regular octagon (8). As the number of sides increases, the polygon approaches a circle.
The key formulas for a regular polygon with n sides of length s are: Area = (n * s²) / (4 * tan(π/n)), Perimeter = n * s, Interior angle = (n - 2) * 180° / n, Apothem = s / (2 * tan(π/n)), and Circumradius = s / (2 * sin(π/n)).
The apothem is the perpendicular distance from the center to the midpoint of any side. The circumradius is the distance from the center to any vertex. These two measurements define the inscribed circle (touching the sides) and circumscribed circle (passing through the vertices), respectively. The area can also be computed as A = (1/2) * perimeter * apothem.